1± 9 14 23 2.0 17 15 32 2.5 17 24 41 3.0 37 41 78 3.5 61 74 135 4.0 114 126 240 4.5 228 234 462 5.0 450 426 876 5.5 787 681 1,468 6.0 789 1,189 1,978 ----- ----- ----- Sum. 2,509 2,824 5,333 It would seem from this that the number of lucid stars in the southern celestial hemisphere is 315 greater than in the northern. But this arises wholly from a seemingly greater number of stars of magnitude 6. In the zone 0° to 30° S., Pickering has 214 stars of this class fewer than Gould. Hence it is not likely that there is any really greater richness of the southern sky. The total number of lucid stars is thus found to be 5,333. But it is not likely that stars of magnitudes 6.1 and 6.2 should be included in this class, though this is done in the above table. From a careful study and comparison of the same data from Pickering and Gould, Schiaparelli enumerated the stars to magnitude 6.0. He found: North pole to 30° S. 3,113 stars. 30° S. to south pole 1,190 stars. ----- Total lucid stars 4,303 For most purposes a classification by entire magnitudes is more instructive than one by half magnitudes. From the third magnitude downward we may assume that 40 per cent. of the stars of each half magnitude belong to the magnitude next above, and 60 per cent. to that next below. We thus find that of Total. Mag. 0 and 1 there are 21 stars 21 Mag. 2 there are 52 stars 73 Mag. 3 there are 157 stars 230 Mag. 4 there are 506 stars 736 Mag. 5 there are 1,740 stars 2,476 Mag. 6 there are 5,171 stars 7,647 Here it is to be remarked that under magnitude 6 are included many other than the lucid stars, namely, all down to magnitude 6.4. The last column gives the entire number of stars down to each order of magnitude. It will be remarked that the number of stars of each order is rather more than three times that of the order next higher. How far does this law extend? Argelander’s ‘Durchmusterung,’ which is supposed to include all stars to magnitude 9.5, gives 315,039 stars for the northern hemisphere, from which it would be inferred that the whole sky contains 630,000 stars to the ninth magnitude. Comparing this with the number 7,647 of stars to the magnitude 6.5, we see that it is forty-fold, so that it would require a ratio of about 3.5 from each magnitude to the next lower. But it is now found that Argelander’s list contains, in the greater part of the heavens, all the stars to the tenth magnitude.